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The abstract of the talk (see below) may be downloaded in one of the following formats:
The Zariski closure operator is naturally defined in any category of
``affine spaces" modelled over an algebra $A$. (See [1] and [2].)
In this talk we look at the algebras on $A = \{0,1\}$ having arbitrary
joins and $\alpha$-meets ($\alpha$ a regular cardinal) and the
topological spaces {\bf Alex($\alpha$)} that they model. Using the
Zariski closure we investigate separated objects, completion
constructions and compactness properties in {\bf Alex($\alpha$)}.
In this way a simple generalization gives rise to a wealth of
interesting examples.
\begin{thebibliography}{2}
\bibitem{Diers99}
Y.~Diers, {\em Affine algebraic sets relative to an algebraic
theory,} Journal of Geometry, {\bf 65} (1999), 329-341.
\bibitem{Giuli2000}
E.~Giuli, {\em Zariski closure, completeness and
compactness,} CatMAT 2000\\ Proceedings:Mathematik-Arbeitspapiere,
Universit\"at Bremen, {\bf 54} (2000), 207--216.
\end{thebibliography}